Skip to content
All articles
electromagnetismphysics

Maxwell's Equations Explained Visually

Four equations that unified electricity, magnetism, and light — and predicted radio waves before they were detected.

10 min read · 2026-06-04

James Clerk Maxwell combined Gauss's law, Faraday's law, and Ampère's law into four vector equations describing how electric fields E and magnetic fields B behave and interact.

The four laws in plain language

Electric charges create electric fields (Gauss). There are no magnetic monopoles — magnetic field lines always close (Gauss for magnetism). Changing magnetic fields create electric fields (Faraday). Currents and changing electric fields create magnetic fields (Ampère-Maxwell).

Light is an electromagnetic wave

Maxwell's equations predict waves traveling at c = 1/√(με) — the speed of light. Light, radio, X-rays, and Wi-Fi are the same phenomenon at different frequencies.

Visualize field lines oscillating in our Visual Studio and hear wave patterns in the Sound Studio on Equation Universe.

Explore interactively

Open equation page